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Author: Bahman Zohuri
Publisher: Springer
ISBN: 3319134760
Category : Technology & Engineering
Languages : en
Pages : 379
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Book Description
This ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book’s coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book’s theoretical explanations and step-by-step mathematical solutions to practical implementations.
Author: Bahman Zohuri
Publisher: Springer
ISBN: 3319134760
Category : Technology & Engineering
Languages : en
Pages : 379
Get Book Here
Book Description
This ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book’s coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book’s theoretical explanations and step-by-step mathematical solutions to practical implementations.
Author: Josef Kuneš
Publisher: Springer Science & Business Media
ISBN: 1907343776
Category : Mathematics
Languages : en
Pages : 451
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Book Description
The present text sets itself in relief to other titles on the subject in that it addresses the means and methodologies versus a narrow specific-task oriented approach. Concepts and their developments which evolved to meet the changing needs of applications are addressed. This approach provides the reader with a general tool-box to apply to their specific needs. Two important tools are presented: dimensional analysis and the similarity analysis methods. The fundamental point of view, enabling one to sort all models, is that of information flux between a model and an original expressed by the similarity and abstraction Each chapter includes original examples and applications. In this respect, the models can be divided into several groups. The following models are dealt with separately by chapter; mathematical and physical models, physical analogues, deterministic, stochastic, and cybernetic computer models. The mathematical models are divided into asymptotic and phenomenological models. The phenomenological models, which can also be called experimental, are usually the result of an experiment on an complex object or process. The variable dimensionless quantities contain information about the real state of boundary conditions, parameter (non-linearity) changes, and other factors. With satisfactory measurement accuracy and experimental strategy, such models are highly credible and can be used, for example in control systems.
Author: Rudolf Kurth
Publisher: Elsevier
ISBN: 1483280209
Category : Science
Languages : en
Pages : 250
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Book Description
Dimensional Analysis and Group Theory in Astrophysics describes how dimensional analysis, refined by mathematical regularity hypotheses, can be applied to purely qualitative physical assumptions. The book focuses on the continuous spectral of the stars and the mass-luminosity relationship. The text discusses the technique of dimensional analysis, covering both relativistic phenomena and the stellar systems. The book also explains the fundamental conclusion of dimensional analysis, wherein the unknown functions shall be given certain specified forms. The Wien and Stefan-Boltzmann Laws can be significant in the systematic application of dimensional analysis to the physics of a single star. The text also discusses group-theoretical reduction of ordinary differential equations and the reductions of the differential equations of stellar structure. The structure of a stellar envelope requires three hypotheses: (1) thermo-nuclear reactions as source of energy of stellar; (2) thermo-nuclear reactions occur at the star's core; and (3) that an envelope surrounding the core exists where no radiation is generated. To complete the model of a star, the investigator should have further assumptions such as the pressure is made-up of gas, radiation, or both. The book can prove helpful for astronomers, astro-physicists, cosmologists, and students of general physics.
Author: John J. Roche
Publisher: Springer Science & Business Media
ISBN: 9780387915814
Category : Mathematics
Languages : en
Pages : 364
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Book Description
The Mathematics of Measurement is a historical survey of the introduction of mathematics to physics and of the branches of mathematics that were developed specifically for handling measurements, including dimensional analysis, error analysis, and the calculus of quantities.
Author: George W. Bluman
Publisher: Springer Science & Business Media
ISBN: 1475743076
Category : Mathematics
Languages : en
Pages : 424
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Book Description
A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag, 1974, by the first author and J.D. Cole. The present book also includes a thorough and comprehensive treatment of Lie groups of tranformations and their various uses for solving ordinary and partial differential equations. No knowledge of group theory is assumed. Emphasis is placed on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This book should be particularly suitable for physicists, applied mathematicians, and engineers. Almost all of the examples are taken from physical and engineering problems including those concerned with heat conduction, wave propagation, and fluid flows. A preliminary version was used as lecture notes for a two-semester course taught by the first author at the University of British Columbia in 1987-88 to graduate and senior undergraduate students in applied mathematics and physics. Chapters 1 to 4 encompass basic material. More specialized topics are covered in Chapters 5 to 7.
Author: Yuri A. Mitropolsky
Publisher: Springer Science & Business Media
ISBN: 9401585350
Category : Mathematics
Languages : en
Pages : 391
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Book Description
This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincaré--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems. This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.
Author: Ronald E Mickens
Publisher: World Scientific Publishing Company
ISBN: 9813202726
Category : Mathematics
Languages : en
Pages : 640
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Book Description
This second edition provides a broad range of methods and concepts required for the analysis and solution of equations which arise in the modeling of phenomena in the natural, engineering, and applied mathematical sciences. It may be used productively by both undergraduate and graduate students, as well as others who wish to learn, understand, and apply these techniques. Detailed discussions are also given for several topics that are not usually included in standard textbooks at this level of presentation: qualitative methods for differential equations, dimensionalization and scaling, elements of asymptotics, difference equations and several perturbation procedures. Further, this second edition includes several new topics covering functional equations, the Lambert-W function, nonstandard sets of periodic functions, and the method of dominant balance. Each chapter contains a large number of worked examples and provides references to the appropriate books and literature.
Author: White
Publisher: McGraw Hill
ISBN: 0077190351
Category : Technology & Engineering
Languages : en
Pages : 794
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Book Description
Overview White's Fluid Mechanics offers students a clear and comprehensive presentation of the material that demonstrates the progression from physical concepts to engineering applications and helps students quickly see the practical importance of fluid mechanics fundamentals. The wide variety of topics gives instructors many options for their course and is a useful resource to students long after graduation. The book’s unique problem-solving approach is presented at the start of the book and carefully integrated in all examples. Students can progress from general ones to those involving design, multiple steps and computer usage. McGraw-Hill Education's Connect, is also available as an optional, add on item. Connect is the only integrated learning system that empowers students by continuously adapting to deliver precisely what they need, when they need it, how they need it, so that class time is more effective. Connect allows the professor to assign homework, quizzes, and tests easily and automatically grades and records the scores of the student's work. Problems are randomized to prevent sharing of answers an may also have a "multi-step solution" which helps move the students' learning along if they experience difficulty. The eighth edition of Fluid Mechanics offers students a clear and comprehensive presentation of the material that demonstrates the progression from physical concepts to engineering applications. The book helps students to see the practical importance of fluid mechanics fundamentals. The wide variety of topics gives instructors many options for their course and is a useful resource to students long after graduation. The problem-solving approach is presented at the start of the book and carefully integrated in all examples. Students can progress from general examples to those involving design, multiple steps, and computer usage.
Author: George Bluman
Publisher: Springer Science & Business Media
ISBN: 0387216499
Category : Mathematics
Languages : en
Pages : 425
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Book Description
This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.
Author: Hans L. Pécseli
Publisher: CRC Press
ISBN: 143987848X
Category : Science
Languages : en
Pages : 578
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Book Description
Winner of an Outstanding Academic Title Award from CHOICE Magazine The result of more than 15 years of lectures in plasma sciences presented at universities in Denmark, Norway, and the United States, Waves and Oscillations in Plasmas addresses central issues in modern plasma sciences. The book covers fluid models as well as kinetic plasma models, including a detailed discussion of, for instance, collisionless Landau damping. Offering a clear separation of linear and nonlinear models, the book can be tailored for readers of varying levels of expertise. Designed to provide basic training in linear as well as nonlinear plasma dynamics, and practical in areas as diverse as the space sciences, laboratory experiments, plasma processing, and more, this book includes: Sections on basic experimental methods, facilitating students’ appreciation of experimental results from laboratory and space plasmas Elements of electromagnetic field theory, fluid mechanics, and wave dynamics, including features of nonlinear wave analysis Basic mathematical tools and other relevant material are summarized in Appendices Exercises as well as short sections that can be used for student presentations A comprehensive reference list reviewing classic papers and notable texts in the field Waves and Oscillations in Plasmas provides a solid foundation in basic plasma physics and its applications, giving a practical introduction to more advanced methods as well. Including simple physical interpretations where possible, this comprehensive, classroom-tested book places plasma sciences in the logical context of general classical physics.
